Natural Frequency of Vibration Test 1

[KevinEgle]

I am attempting to find the natural frequency of a test fixture and sample on a shaker. When a test sweep is performed with an output force of 1 g, the natural frequency of the system (2 part fixture and test piece) is found to be approximately 460 Hz. When the force is increased to 4 g, the natural frequency drops to around 200 Hz, and when increased to 8 g, the natural frequency is found to be less than 150 Hz. What might cause such a drastic change? Does the effective mass of the system change with increasing g levels?

 

[MikeyP]

If the test structure is not obviously non-linear (ie no obvious sources of geometric stiffening, friction, clearance, viscoelastic behaviour etc.) and your test set-up is OK, then the source of the problem must be the shaker.

1) You should measure the applied force (if you are not already doing so) by placing a load cell between the shaker and the structure, you can then calculate an accelerance FRF (acceleration divided by applied force). This will minimise any shaker-structure interactions (force dropout, caused by an interaction with the shaker can show apparent downward shifts in natural frequency).

2) Use the smallest shaker you can, whilst still retaining the required response level, this will minimise the mass and stiffness loading due to the shaker attachment.

3) Ensure that the displacement of the shaker armature is not so great that it is "bottoming out", and hence inducing non-linear behaviour. A shaker will still behave non-linearly at large displacements even if it is not bottoming out because the length of armature coil within the magnetic field is reduced at high displacement.

4) Check that the shaker is properly grounded mechanically.

5) Use a slower sweep rate on the excitation signal to mimimise transient effects (or use random or stepped-sine excitation)

M

 

[electricpete]

Just thinking out loud on this one....
(I don't have any practical experience with shakers)

If amplitude is truly the only thing changing, and If the system were linear, the resonant frequency should not change with amplitude.

Therefore it seems logical to conclude that a non-linearity is dramatically effecting your system. For instance a looseness.

Here's an example I'm thinking of. Take a large box with a small but heavy weight inside free to slide around on the bottom of the box. Shake the box back and forth horizontally. If you shake the box with small displacement, the weight will try to stay where it is and slide relative to the box. The only mass that is being accelerated is the mass of the box. But if you shake the box with large displacement, the weight will hit the edges and have to be accelerated. The total mass being accelerated looks higher and the apparent natural frequency may go down (as well as harmonics showing up from the impacts).

If there is some looseness at work, it may be detected by looking at the spectrum. Usually looseness will be accompanied by harmonics.

I suspect there are other types of non-linearities which are more subtle than looseness. Also perhaps worthwhile to check your setup carefully.

 

[IRstuff]

Is your sample top-heavy and are you using a slip-table?

The oil film that the table rides on behaves like a damped spring.

TTFN

 

[KevinEgle]

No, the sample is definitely not top heavy - the fixture is a solid aluminum block, and the part is just a plastic air cleaner. We are testing in the vertical direction, with no slip table. We have mounted additional accelerometer channels on different portions of the set up, and are currently re-sweeping the part.

 

[Hatch]

Just a quick question. Does the mode shape change with each natural frequency? C. Hugh (

http://www.Hatch.ca)

 

[KevinEgle]

The mode shape is different for each of the three tests - from what I am told, the setup (accels, cables, ect) have been changed, and the results were the same.

 

[IRstuff]

does the natural frequency actually move or is it a new peak with the old one still there?

TTFN

 

[GregLocock]

1g (Hang on do you mean an acceleration of 1g on the part - that is an acceleration, not a force) is one hell of an input for a modal test. I'm with Mike on this one it sounds more like a shaker problem than a weakening spring effect in the test part. I've tested a few airboxes in my time and can't remember any severe non linearity - the damping at the joint that clamps the filter itself to the box being the main cause of difficulty.

480 hz is way too high for the first frequency, or else you have a very well designed box.



Cheers

Greg Locock

 

[KevinEgle]

The plot is full of peaks, and they don't seem to change that much depending on the input. It's just a matter of which one is the most pronounced during a run.

Now that I am looking at the plots of the sweeps I did, the shape doesn't appear to have changed that much between them. Like I said, it's a matter of which one is most pronounced

 

[MikeyP]

Can you clearly describe your test set-up? I am particularly interested to know:

(1) where the force transducer (if you are using one) is placed.

(2) if you are measuring an acceleration spectrum, PSD or FRF

(3) the number of averages you are taking of the spectrum/PSD/FRF

(4) the type of data aquisition and analysis equipment/software you are using.

It would be easier to help if you gave more information.

M

 

[vanstoja]

Your major problem appears to be that you are looking for THE ONE AND ONLY natural frequency of an apparently somewhat complex two-component system while you are exciting possibly several modes of each component's responses by jacking up the input accelerations. Did you do any pretest analysis of both the fixture and the black box attached to it to be able pick out the fundamental response peak of any of the several modes that you may be exciting? Personally, I wouldn't enter into a test of this kind without having done some analysis beforehand to predict the results that might show up. Now you're shooting in the dark.

 

[KevinEgle]

The two piece fixture was put through a one g resonance sweep before the test, and no resonance response was noted until 500 + hertz, with the lowest peak being at 1800.

 

[KevinEgle]

Ok, let's see if I can answer all these questions for MikeyP

1) There is no force transducer. The only thing being measured is acceleration

2) PSD

3) I am not particularly familiar with the VWIN Software we are using, so I couldn't find the answer that that question.

4) See number 3

 

[MikeyP]

Thanks for the info Kevin.

If you are not measuring the applied force then you have to be sure that the excitation signal you are applying is identical every time. The shaker itself will be non-linear, so if you apply a sweep with a voltage amplitude of 1v, then a a subsequent test with a voltage amplitude of 2v will not necessarily produce twice the force. Also, even though the applied voltage may have the same amplitude at all frequencies, the resulting force may not. Again the frequency content may also change when you change the excitation level, due to shaker non-linearity and shaker-structure interaction.

Therefore, I would not expect the relative heights of the peaks in the PSD to be the same at different excitation levels

Another thing puzzles me about the level of excitation you are applying. You quote excitation levels of 1g 4g 8g etc. Is this the acceleration of the fixture at some frequency or other? Or the response level at one of the peaks, or what? How do you "know" what voltage to apply to the shaker to obtain this level of response?

The way I would do it (without resorting to a full-blown modal test) would be as follows:

Put a force transducer either between the shaker and the fixture or between the fixture and the filter (assuming the filter is only attached to the fixture at one point). This then gives you a reference to compare the response with. In fact, thinking on my feet, if you don't have a force transducer, you could place an accelerometer on the fixture (as long as the 500+ Hz where you start to notice resonant behaviour of the fixture is well above the frequency range of interest). You could then use this accelerometer as am "input" reference and measure the transfer function between this accelerometer and the others positioned on the filter. Note however, that the transfer function is calculated by dividing each of the response acceleration spectra by the spectrum of the reference transducer (force or acceleration). Note that you divide spectra NOT the PSD. In this way you are quite literally taking the shaker characteristics out of the equation.

Secondly, I would use a random excitation or stepped sine rather than a sweep. That way you measure the steady state response without any transient effects. The signal processing is more difficult though and your equipment may not be capapble of it. If you are still using the sweep test then keep the sweep rate as low as possible to minimise the transient effects and start/end the sweep well below/above the frequency range of interest and discard the results outside your range.

Thirdly, (assuming we are sticking with the sweep test) I would perform several measurements at each excitation level and average the resulting transfer functions (there will be one transfer function for each response accelerometer, each comprising a magnitude and a phase characteristic). A measurement will never be the same twice due to noise and other enviromental factors. Averaging helps to minimise any random noise (I would say do 10 or so averages as a minimum for an accurate result).

Fourthly, I would specify a particular input voltage amplitude for the sweep signal going to the shaker, and vary that for each round of tests (say 1v, 2v, 4v, 8v, or other suitable voltages, instead of your 1g, 2g, 4g, 8g, etc). You will then end up with a series of transfer functions at each voltage excitation level.

For example: If you have say 6 response accelerometers positioned on the filter labled A1...A6 and one reference accelerometer on the fixture, Ar, then set the amplitude voltage of the sweep signal going into the shaker at 1v. Measure the spectra of each accelerometer and calculate the transfer functions A1/Ar, A2/Ar ... A6/Ar. These will be complex transfer functions. Do the test again 10 times and average the transfer function for each accelerometer, ie.
[A1(run1)/Ar(run1) + A1(run2)/Ar(run2) + ... + A1(run10)/Ar(run10)]/10
and
[A2(run1)/Ar(run1) + A2(run2)/Ar(run2) + ... + A2(run10)/Ar(run10)]/10
and so on until
[A6(run1)/Ar(run1) + A6(run2)/Ar(run2) + ... + A6(run10)/Ar(run10)]/10

This yields 6 averaged complex (ie magnitude and phase) transfer functions for a shaker input amplitude of 1v,
T1(1v), T2(1v) ... T6(1v).

You can then repeat the whole process with an amplitue of 2v, 4v, 8v etc. (I am using these voltages as examples, not specifically recommending the levels that you require).

You can then compre the transfer functions and look for differences. T1(1v), T1(2v), T1(4v) etc should have very nearly the same magnitude and phase characteristics, as should T2(1v), T2(2v), T2(4v) etc., always comparing like with like.

If there are still major differences in the height of the peaks in the transfer function amplitude characteristic between excitation levels then you can be almost certain (because you have been so careful in the design of your experiment) that it is due to non-linearity in the test piece or fixture and you don't have to worry about the shaker at all.

Hope this helps

M